a) Find the definite integrals of the following functions (i) Sx(x² +9)10 dx (ii) xp xu)x (iii) S 20x³/(x* +9) dx (iv) S10xe* dx

Q: x²+1 Find J+3x+1 11.

A:

Q: Factor x* + 1 as a difference of squares by first adding and subtracting the same quantity. Use this…

A:

Q: 9-x2 x dx

A: ∫9-x2x2dx=∫cot2udu=∫ -1+csc2udu=-∫ 1du+∫csc2udu=-u-cotuSubstitute back…

Q: S(x*+1)(x* + 5x)'dx 11.

A:

Q: 9. f²-2x(3x - 1) dx

A:

Q: Differentiate. y= In [(x + 4)(5x– 6)(3 – x)] d dy In ((x+ 4)(5x – 6)(3–x))) = |

A: Given: To find: The derivative of the given function.

Q: 1. f4x-³ dx -3

A: Find the integral

Q: Find f. f"(x)  =2/3x2/3

A:

Q: Find f. f"(x)  =20x3 -12x2 +6x

A: Consider the provided function, f''x=20x3-12x2+6x Find  fx. Integrate both the sides with respect to…

Q: -sech? (In 3.x)

A: We can find the answer as below.

Q: [5x(4-2x²) dx

A: To evaluate the given integral

Q: Find f. f"(x)  =x6 - 4x4 +x +1

A: ∫xndx = xn+1n+1+C

Q: -1)/(x4))1/2

A:

Q: Find f'(x) and simplify. f(x) = (0.2x + 2)(0.6x - 9) Which of the following shows the correct…

A: f(x)= (0.2x+2)(0.6x-9)

Q: 12. 3x"(x1222 - 1300) dx 13. 3x – 4x + 1 dx

A: Topic-integration

Q: find -3/2 x74] x dx

A:

Q: evalu ate the integ ho ral (Usec for Hhe constant of integ ra (In (x))²dx

A:

Q: Find ∫ dx / √(4x2 + 1)

A: Given: ∫14x2+1dx

Q: x² + 8x + 5 x³ + 8x / dx

A:

Q: | A = S² - (x - 1)³ dx + S³² (x-1)³ dx

A: We have to solve the given definite integral.

Q: 7. Inx dx

A: We need to evaluate definite integral.

Q: (4 - x2)3/2 dx 3

A: Consider, I=423∫-22(4-x2)3/2dx I =4232∫02(4-x2)3/2 dx   since f(x) is even function that is…